There are actually many many people who are both socially anxious and extraverted. Really not uncommon. It doesn't look like that because introversion and social anxiety are so often mixed up - just like in this article. Keep in mind those psychological concepts are defined by the inner workings and motivations of people's minds, not by behavior observable from the outside.

Introversion: This person gets energy from being alone or with close friends in a routine situation. (Not the same as being lonely, mind!). They feel attracted by situations and environments promising those situations.

Extraversion: This person recharges by mingling with other people. From small talk at the water cooler to larger social gatherings. They feel attracted by social gatherings, and want to be part of them.

Social Anxiety: This person is anxious in social gatherings (of people not being close friends or family). They have feelings of inadequacy about themselves as social beings, and fear being devalued for acting wrong or - worse - being wrong.

Those concepts are related but not at all the same. Persons being both extraverted and socially anxious long for social situations involving new people, but at the same time feel inadequate of being in them. Or ruminate about their behaviour afterwards. Or actively try to get comments of positive validation from their peers during or after the gathering.

At the same time people can be introverted and not socially anxious at all. I have a colleague like that: loves working alone, doesn't need companions even for longer, more demanding projects, but at the same time has zero qualms leading a team, talking to customers, going in front of unknown audiences. It just exhausts them.

Introversion and Extraversion are concepts involving motivations: What situations do people feel attracted to.

Anxiety is essentially about fear of inadequacy, or perceived lack of agency about a situation. So not about motivation, but about a concept of self.

There are, of course, feedback loops enabling correlations like the introversion + social anxiety one. Children (adults too, for that matter) have multiple avenues of gaining validation and positive experience in live, e.g. social competency (as colleague, parent, friend, community member,...), physical performance (sports, crafting, ...), intellectual performance and so on. If they learn that they are good at a thing, they tend to do that thing more often, because the experience of competency feels good. They will experience these kinds of situations more, and thus gain more competency in these kinds of situations.

Now if a child is often ill, and can't go play outside with their peers, it won't do nothing inside, but instead probably be reading or drawing or crafting. So it will not learn social skills at that time, but will get better at drawing and crafting. If it already had a tendency to introversion, that tendency will probably get stronger.

OTOH imagine a child that was very socially active in early childhood, but then , around 12 years old, the parents moved and the child had to change schools, and got bullied in the new school. This kid probably was extraverted and now gained strong feelings of social inadequacy, of not belonging, of being somehow different or wrong as a person. They will still feel attracted to social situations, but thanks to their experience of being bullied, this will feel very stressful to them. Extraverted and socially anxious.